The Physics Philes, lesson 113: Don’t Interfere (Or Do)

So far in our discussion of waves we’ve basically been working with one wave at a time. But that’s not really how waves work in real life. Waves from different sources are constantly bouncing around. Modern life is a cacophony. Physics can tell us how those waves interact.

With all the waves flying around, some of those waves are going to overlap. This is called interference, and we’ve seen hints of this interaction in our earlier discussions of nodes, antinodes, and standing waves. In that case, two waves flowing in opposite directions combine to produce a standing wave. The points at which the absolute value of the amplitude are highest and lowest do not change.

There are two types of interference: constructive and destructive. Let’s pretend that we have two speakers and you are standing an equal distance away from both of them. The waves coming from each speaker take the same time to reach your ears and arrive in phase. The amplitude of that sound is twice what it would be if you just had one speaker. This is constructive interference.

What happens, then, if the waves don’t travel and equal distance? Let’s say that you move so it takes a speaker a half wavelength longer to reach your ears. In this case, the waves are a half cycle off; they are out of phase. The crest of one wave arrives at the same time as the trough of the other and end up canceling each other out. This means that the amplitude of the wave is going to be lower than it would be with only one speaker. This is called destructive interference.

You’ve probably deduced by now when we will see constructive interference and when we will see destructive interference. Since in our little thought experiment we found that the amplitude is greater when the waves are in phase, it makes sense that we’d get constructive interference when the distances traveled by the waves differs by a whole number multiple of the wavelength. In those situations the waves are in phase. If the distance causes the waves to be off by a half integer multiple of the wavelength – like 1/2, 3/2, 5/2, etc. – then the wave will arrive out of phase and there will be destructive interference. Little or no sound will reach your ears if this happens.

This isn’t just a physical curiosity of waves. While it is super cool, there are actually practical applications for our understanding of constructive and destructive interference. We can use this knowledge to make loud things quieter. Using destructive interference, we can use more sound to cancel out unwanted sound. It’s one of those weird situations where more is less.

All of this, I should mention, happens when the two sound waves in question have the same frequency. But what happens if those two waves don’t have the same frequency? What happens then? You’ll just have to come back next week to find out.

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